Reconfiguring 10-Colourings of Planar Graphs

Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every in...
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Autor*in:	Feghali, Carl [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Graph colouring Reconfiguration graph Planar graph

Übergeordnetes Werk:	Enthalten in: Graphs and combinatorics - Tokyo : Springer-Verl. Tokyo, 1985, 36(2020), 6 vom: 30. Mai, Seite 1815-1818
Übergeordnetes Werk:	volume:36 ; year:2020 ; number:6 ; day:30 ; month:05 ; pages:1815-1818

Links:	Volltext

DOI / URN:	10.1007/s00373-020-02199-0

Katalog-ID:	SPR041374371

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520			\|a Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$.
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773	0	8	\|i Enthalten in \|t Graphs and combinatorics \|d Tokyo : Springer-Verl. Tokyo, 1985 \|g 36(2020), 6 vom: 30. Mai, Seite 1815-1818 \|w (DE-627)30018381X \|w (DE-600)1481435-3 \|x 1435-5914 \|7 nnns
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912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
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912			\|a GBV_ILN_4338
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author_variant	c f cf
matchkey_str	article:14355914:2020----::eofgrn1cluigo
hierarchy_sort_str	2020
bklnumber	31.12
publishDate	2020
allfields	10.1007/s00373-020-02199-0 doi (DE-627)SPR041374371 (SPR)s00373-020-02199-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 31.12 bkl Feghali, Carl verfasserin aut Reconfiguring 10-Colourings of Planar Graphs 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$. Graph colouring (dpeaa)DE-He213 Reconfiguration graph (dpeaa)DE-He213 Planar graph (dpeaa)DE-He213 Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 36(2020), 6 vom: 30. Mai, Seite 1815-1818 (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:36 year:2020 number:6 day:30 month:05 pages:1815-1818 https://dx.doi.org/10.1007/s00373-020-02199-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE AR 36 2020 6 30 05 1815-1818
spelling	10.1007/s00373-020-02199-0 doi (DE-627)SPR041374371 (SPR)s00373-020-02199-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 31.12 bkl Feghali, Carl verfasserin aut Reconfiguring 10-Colourings of Planar Graphs 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$. Graph colouring (dpeaa)DE-He213 Reconfiguration graph (dpeaa)DE-He213 Planar graph (dpeaa)DE-He213 Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 36(2020), 6 vom: 30. Mai, Seite 1815-1818 (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:36 year:2020 number:6 day:30 month:05 pages:1815-1818 https://dx.doi.org/10.1007/s00373-020-02199-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE AR 36 2020 6 30 05 1815-1818
allfields_unstemmed	10.1007/s00373-020-02199-0 doi (DE-627)SPR041374371 (SPR)s00373-020-02199-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 31.12 bkl Feghali, Carl verfasserin aut Reconfiguring 10-Colourings of Planar Graphs 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$. Graph colouring (dpeaa)DE-He213 Reconfiguration graph (dpeaa)DE-He213 Planar graph (dpeaa)DE-He213 Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 36(2020), 6 vom: 30. Mai, Seite 1815-1818 (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:36 year:2020 number:6 day:30 month:05 pages:1815-1818 https://dx.doi.org/10.1007/s00373-020-02199-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE AR 36 2020 6 30 05 1815-1818
allfieldsGer	10.1007/s00373-020-02199-0 doi (DE-627)SPR041374371 (SPR)s00373-020-02199-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 31.12 bkl Feghali, Carl verfasserin aut Reconfiguring 10-Colourings of Planar Graphs 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$. Graph colouring (dpeaa)DE-He213 Reconfiguration graph (dpeaa)DE-He213 Planar graph (dpeaa)DE-He213 Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 36(2020), 6 vom: 30. Mai, Seite 1815-1818 (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:36 year:2020 number:6 day:30 month:05 pages:1815-1818 https://dx.doi.org/10.1007/s00373-020-02199-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE AR 36 2020 6 30 05 1815-1818
allfieldsSound	10.1007/s00373-020-02199-0 doi (DE-627)SPR041374371 (SPR)s00373-020-02199-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 31.12 bkl Feghali, Carl verfasserin aut Reconfiguring 10-Colourings of Planar Graphs 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$. Graph colouring (dpeaa)DE-He213 Reconfiguration graph (dpeaa)DE-He213 Planar graph (dpeaa)DE-He213 Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 36(2020), 6 vom: 30. Mai, Seite 1815-1818 (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:36 year:2020 number:6 day:30 month:05 pages:1815-1818 https://dx.doi.org/10.1007/s00373-020-02199-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.12 ASE AR 36 2020 6 30 05 1815-1818
language	English
source	Enthalten in Graphs and combinatorics 36(2020), 6 vom: 30. Mai, Seite 1815-1818 volume:36 year:2020 number:6 day:30 month:05 pages:1815-1818
sourceStr	Enthalten in Graphs and combinatorics 36(2020), 6 vom: 30. Mai, Seite 1815-1818 volume:36 year:2020 number:6 day:30 month:05 pages:1815-1818
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Graph colouring Reconfiguration graph Planar graph
dewey-raw	510
isfreeaccess_bool	false
container_title	Graphs and combinatorics
authorswithroles_txt_mv	Feghali, Carl @@aut@@
publishDateDaySort_date	2020-05-30T00:00:00Z
hierarchy_top_id	30018381X
dewey-sort	3510
id	SPR041374371
language_de	englisch
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author	Feghali, Carl
spellingShingle	Feghali, Carl ddc 510 bkl 31.12 misc Graph colouring misc Reconfiguration graph misc Planar graph Reconfiguring 10-Colourings of Planar Graphs
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topic_title	510 ASE 31.12 bkl Reconfiguring 10-Colourings of Planar Graphs Graph colouring (dpeaa)DE-He213 Reconfiguration graph (dpeaa)DE-He213 Planar graph (dpeaa)DE-He213
topic	ddc 510 bkl 31.12 misc Graph colouring misc Reconfiguration graph misc Planar graph
topic_unstemmed	ddc 510 bkl 31.12 misc Graph colouring misc Reconfiguration graph misc Planar graph
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title	Reconfiguring 10-Colourings of Planar Graphs
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title_full	Reconfiguring 10-Colourings of Planar Graphs
author_sort	Feghali, Carl
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title_sort	reconfiguring 10-colourings of planar graphs
title_auth	Reconfiguring 10-Colourings of Planar Graphs
abstract	Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$.
abstractGer	Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$.
abstract_unstemmed	Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$.
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title_short	Reconfiguring 10-Colourings of Planar Graphs
url	https://dx.doi.org/10.1007/s00373-020-02199-0
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doi_str	10.1007/s00373-020-02199-0
up_date	2024-07-03T21:48:11.948Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR041374371</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220110175507.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201102s2020 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00373-020-02199-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR041374371</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00373-020-02199-0-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.12</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Feghali, Carl</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Reconfiguring 10-Colourings of Planar Graphs</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let %$k \ge 1%$ be an integer. The reconfiguration graph %$R_k(G)%$ of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer %$\ell \ge k + 2%$ and k-degenerate graph G on n vertices, %$R_{\ell }(G)%$ has diameter %$O(n^2)%$. The conjecture has been verified only when %$\ell \ge 2k + 1%$. We give a simple proof that if G is a planar graph on n vertices, then %$R_{10}(G)%$ has diameter at most %$n(n + 1)/ 2%$. Since planar graphs are 5-degenerate, this affirms Cereceda’s conjecture for planar graphs in the case %$\ell = 2k%$.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Graph colouring</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Reconfiguration graph</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Planar graph</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Graphs and combinatorics</subfield><subfield code="d">Tokyo : Springer-Verl. Tokyo, 1985</subfield><subfield code="g">36(2020), 6 vom: 30. 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